the number of people p(t) (in hundreds) infected t days after an epidemic begins is approximated by p(t) = 5-35t-5/2t^2. When will the number of people infected start to decline

Question

campbell_st · Answer

the function p(t) is parabolic, and concave down, so the decline will occur to the right of the line of symmetry. 

or to the right of the value of x which gives the maximum value. 

so 2 methods available. 

Do you know calculus... particularly how to differentiate..?

anonymous · Answer

indeed i do, im confused where to start though

campbell_st · Answer

ok... find the 1st derivative... and then let it equal zero... 

solve for t

does that make sense..?

anonymous · Answer

yes it does, thank you, since there is division within it, do i make it quotient rule?

campbell_st · Answer

to me it looks like 

$$p(t) = 5 - 35t - \frac{5t^2}{2}$$

campbell_st · Answer

so

$$p'(t) = -35 - 5t$$

anonymous · Answer

kinda the 5/2 and the t^2 is next to eahc other its more like (5/2)t^2

campbell_st · Answer

ummm doesn't make a lot of sense as time ends up being negative... which it can't be. 

can you check to see if there is a typo in the question...

anonymous · Answer

$$p(t) = 5- 35t - \frac{ 5 }{ 2 } t^2$$

campbell_st · Answer

ummm odd question given that t is negative... 

$$p'(t) = -5(7 + t)$$

so t = -7 is the value that gives the maximum..so  t>-7 is when the infection starts to decline